# Questions tagged [automorphism-group]

For finding, constructing and proving results about automorphisms and applying them into different contexts. An automorphism is an isomorphism from an object to itself, and collectively they form a group under composition of mappings. Sometimes the only automorphism is the trivial one (the identity map), but often structures will have interesting/non-trivial automorphisms.

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### automorphism group of splitting field of cubic polynomial over $\mathbb{Q}$

The question is to compute the isomorphism class of automorphism group of the splitting field over $\mathbb{Q}$ of $x^3 - 6x + 2$. I know that this polynomial is irreducible over $\mathbb{Q}$ by ...
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### Burnside groups : a few questions

Let $G=B(n,e)=F_n/\langle\langle F_n^e\rangle\rangle$ be the Burnside group on $n$ generators with exponent $e$, i.e. the quotient of the free group on $n$ generators $F_n$ by the normal subgroup ...
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### Find the order of $\operatorname {Aut}(C_p^{\oplus n})$

Let $C_p$ be a cyclic group of prime order $p$. Find the number of the automorphism group of $C_p^{\oplus n}$. Is this approach correct? $C_p$ is isomorphic to $(\mathbb Z_p,+)$. The automorphism ...
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